[logo] [logo]

Unicorn Trading
Expectancy Score vs Sharpe Ratio
by Alex Matulich

| Home | ProSizer | EasyLanguage | Quotes |

Expectancy Score

Back when I set out to develop my own trading system, two different successful traders recommended that I read Trade Your Way to Financial Freedom by Van K. Tharp. One trader recommended it to me as a good book on position sizing. In spite of its sensationalist title, it's a good book, for no other reason than it contains a valuable feature: how to measure "quality" of a trading strategy objectively, in terms of expectancy multiplied by opportunity. I call this the "expectancy score."

Expectancy is how much you expect to earn from each trade for every dollar you risk. Opportunity is how often your strategy trades. You want to maximize the product of both.

Expectancy = (AW × PW + AL × PL) ⁄ |AL|
(expected profit per dollar risked)
Expectancy score = Expectancy × Opportunity
AW = average winning trade (excluding maximum win)
PW = probability of winning (PW = <wins>NST
      where <wins> is total wins excluding maximum win)
AL = average losing trade (negative, excluding scratch losses)
|AL| = absolute value of AL
PL = probability of losing (PL = <non-scratch losses>NST)
Opportunity = NST × 365 ⁄ studydays   (opportunities to trade in a year)

It is important to have the |AL| in the denominator of expectancy because this converts the expectancy to "risk units" — earnings per dollar risked.

This calculation of expectancy score, as described above, is different than that described by Tharp in three respects:

Expectancy and Position Sizing

The expectancy score described above complements position sizing. You have to make a paradigm shift away from evaluating strategies based on net profit. Forget the net profit, forget drawdown, forget number of wins in a row, forget everything else Tradestation shows you in the Strategy Summary. These things mean nothing for strategy comparisons, because everyone has a subjective opinion about which of those measurements matter most.

In your mind you must decouple the entry/exit rules from "net profit" performance or "annualized return" performance. Instead, think of a strategy like this:

So when you're designing the entry/exit rules and their input parameters, don't optimize for net profit! Instead . . .

Optimize for Expectancy Score

Optimize for maximum expectancy score, without regard to anything else. Position sizing takes care of the rest. A good position sizing strategy will result in greater, more consistent profits on a high-expectancy strategy than on a low-expectancy strategy, even if the low-expectancy strategy has a higher net profit on a 1-contract basis!

Now, I know some trading software packages let you optimize strategy parameters based on anything you want. TradeStation gives you only canned results like net profit, win/loss ratio, drawdown, etc. For those of us who use TradeStation, I developed something that lets me optimize my strategies on expectancy score.

It's an EasyLanguage function (_SystemQuality). You just stick it at the end of your signal and start the optimizer. Every iteration of the optimizer will cause a line to be written to an Excel .csv file. Then all you do is load it into Excel, sort by the last column, and voila! The parameters for maximum expectancy score are right at the top.

The documentation included with the source code is detailed and should explain everything more fully. This function can be modified to use in optimizing anything else you want, also.

Sharpe Ratio

Some people like to use the Sharpe Ratio to gauge the relative quality of one trading strategy compared to another. After extensive research, I have no choice but to conclude that the Sharpe ratio isn't useful for objectively evaluating the merit of a system. It does have uses, but I do not agree that it should be used for determining overall merit.

Take two extremes for example:

Which system would you rather trade? System A has a higher Sharpe ratio — it's actually infinite due to zero standard deviations in returns. Personally I'll take system B over A any day! I am more concerned with my equity growth and earning power of my risk capital, than whether periodic returns are exactly the same.

All the Sharpe ratio does is measure consistency. True, that's one element of merit, but certainly not the whole picture. Using it to determine the merit of a whole trading strategy results in completely erroneous and subjective evaluations, as demonstrated by the extreme example above.

There's really only one objective way to measure the merit of a system, and that's how much you expect it to earn for every dollar risked combined with how often it gives you the opportunity to earn that expected return. The risk concept is important; you're measuring the return from your risk capital (i.e. your initial stoploss), not what you actually "invest" in the market.

Develop a system that has a high expectancy score, and you'll find that the Sharpe ratio takes care of itself.

My research has led me down some fruitful paths, and some fruitless paths. Optimizing for Sharpe ratio is in the latter category.

| Home | ProSizer | EasyLanguage | Quotes |

[logo] [logo]

Copyright © 2004 by Unicorn Research Corporation
All rights reserved.